ERROR AND UNCERTAINTY QUANTIFICATION AND SENSITIVITY ANALYSIS IN MECHANICS COMPUTATIONAL MODELS

Abstract

Multiple sources of errors and uncertainty arise in mechanics computationalmodels and contribute to the uncertainty in the final model prediction.This paper develops a systematic error quantification methodologyfor computational models. Some types of errors are deterministic,and some are stochastic. Appropriate procedures are developed toeither correct the model prediction for deterministic errors or toaccount for the stochastic errors through sampling. First, inputerror, discretization error in finite element analysis (FEA), surrogatemodel error, and output measurement error are consid- ered. Next,uncertainty quantification error, which arises due to the use ofsampling-based methods, is also investigated. Model form error isestimated based on the comparison of corrected model prediction againstphysical observations and after accounting for solution approximationerrors, uncertainty quantification errors, and experimental errors(input and output). Both local and global sensitivity measures areinvestigated to estimate and rank the contribution of each sourceof error to the uncertainty in the final result. Two numerical examplesare used to demonstrate the proposed methodology by considering mechanicalstress analysis and fatigue crack growth analysis.